To expand the expression \((5x + 2)(3y - z)\), we will use the distributive property (also known as the FOIL method for binomials):

\[
(5x + 2)(3y - z) = 5x(3y - z) + 2(3y - z)
\]

Now distribute each term in the first binomial to each term in the second binomial:

\[
5x(3y - z) = 5x \cdot 3y - 5x \cdot z = 15xy - 5xz
\]

\[
2(3y - z) = 2 \cdot 3y - 2 \cdot z = 6y - 2z
\]

Combine all the terms:

\[
15xy - 5xz + 6y - 2z
\]

So, the expanded form of \((5x + 2)(3y - z)\) is:

\[
15xy - 5xz + 6y - 2z
\]

Would you like more details or have any questions? 

Here are some related questions for further exploration:

1. How do you expand \((4x - 3)(2y + 5)\)?
2. What is the result of expanding \((7x + 2)(4y - 3z)\)?
3. How do you simplify the expression \((2a + 3b)(5c - d)\)?
4. What are the steps to expand \((3x - 4)(y + 2)\)?
5. Can you explain the FOIL method in more detail?
6. How would you expand and simplify \((6m + 2n)(3p - q)\)?
7. What is the expanded form of \((x + 1)(x - 1)\)?
8. How do you verify your answer after expanding an expression?

**Tip:** When expanding binomials, be systematic in your approach to ensure that each term in the first binomial is multiplied by each term in the second binomial.

Learn how to expand the expression (5x + 2)(3y - z) using the distributive property. This problem covers the binomial expansion method and the distributive property in algebra. Suitable for students in Grades 7-9.

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